Musk also confronted his "fateful" tweet on August 8 when he posted that he was taking Tesla private – a move he said he did not regret.
"Am considering taking Tesla private at US$420. Funding secured," Musk tweeted, following up with "good morning" and a smiley emoji.
His tweet set off a chain reaction which saw Tesla's shares climb 6.8 per cent to US$365.36.
However, the following day investigators in the San Francisco office of the Securities and Exchange Commission asked Tesla for explanations.
Musk's "funding secured" statement suddenly put him at risk of violating securities laws. He provided no details about how much funding had been secured, from whom or under what conditions. His email to employees did not mention anything about the funding.
"That's a clear factual statement," said John C. Coffee Jr., a professor at Columbia Law School who specialises in corporate law and securities fraud. "If it's not fully secure, that's potentially a very material misrepresentation, and a very straightforward violation of Rule 10b-5" of the securities law — in short, securities fraud.
It is illegal for a director or officer of a public company "to knowingly or recklessly make material misstatements about that company," said John Coates, a professor at Harvard Law School who teaches mergers and acquisitions.
Musk's "tweets seem cryptic at best, and it is hard to see how he has complied with his duty to not be misleadingly incomplete."
Tesla declined to comment on the matter.
Two weeks prior to Musk's tweet it was revealed Tesla had burned through US$739.5 million in cash on its way to a record US$717.5m net loss in the second quarter, as it cranked out more electric cars.
Tesla has spent millions as it reached a goal of producing 5,000 Model 3 sedans per week by the end of June. The company says production is rising, with the goal of 6,000 per week by the end of August.
Musk has also found himself in hot water this year from comments he has made through social media.
The billionaire apologised after coming under scrutiny for calling one of the divers involved in rescuing a Thai soccer team from a flooded cave, a "pedo".
- With AP and Washington Post